Question

POQ is a line ray OR is perpendicular to line PQ, OS is another ray lying between rays OP and OR.

Prove that angle ROS = ½ (angle QOS – angle POS)​

Answer 1

$\huge{\underline{\bigstar{\sf{solution!!}}}}$

∠ROS = 90° - ∠POS - (i)

∠QOS = ∠QOR + ∠ROS =90° + ∠ROS

⇛ 90° = ∠QOS - ∠ROS - (ii)

Substituting (ii) in (i) we get

∠ROS = ∠QOS - ∠ROS - ∠POS

⇛ 2 ∠ ROS = ∠QOS - ∠ POS

$⇛ ∠ROS\ frac {1}{2} (∠QOS-∠POS)$

Hence proved